American troops struggle on to a beach in Normandy, where ‘thousands were machine-gunned as they waded ashore, like ducks in a shooting gallery.’ Photograph: Hulton-Deutsch/Corbis

Early on the evening of 5 June 1944, the BBC broadcast a coded message to Resistance units in Nazi-occupied France. "Les dés sont sur le tapis" ("The dice are down") the announcer said and then, a few moments later: "Il fait chaud à Suez." It was the signal that the Resistance had been waiting for - for them to attack the Germans' lines of communication because the greatest naval invasion in history was at hand. Across the Channel, the final preparations were underway. Shortly before midnight, in towns and villages across southern England, the air filled with the roar of hundreds of aircraft engines. Thousands of people in their dressing gowns and pyjamas went out into their back gardens, staring up into the sky at the vast armada silhouetted against the clouds. Some dropped to their knees and prayed for success; others simply said: "This is it" and went back to bed.

In the waters just off Southampton, some 5,000 landing craft, escorted by battleships, cruisers and destroyers and carrying 130,000 men, were already moving south. On one ship, the army chaplain prepared for a service in front of a small silver cross, but as he was about to begin, a gust of wind whipped the cross off the table on to the deck, where it broke in two. "What an omen!" one observer wrote later. "For the first time I realised what 'fear of God' really was. All around, men were looking completely shattered."

We are all familiar now with the story of D-Day: the soldiers vomiting in their tossing landing crafts, the sudden lurch on to the sands, the slaughter on Omaha Beach, the exhaustion, heroism, shock and courage captured in the opening sequence of Steven Spielberg's film Saving Private Ryan. The prospect of yet another account of the same events is not immediately attractive, not least because so much popular military history is so tediously and unimaginatively written.

But Antony Beevor is not just any military historian: as a master of narrative, expertly blending the grand sweep with the telling anecdote, he has few peers. Though his style seems terse, it is the detail that drags you in: the officers eating breakfast on deck before the landing, with a steward asking: "Porridge or cereal this morning, sir?"; the German soldiers cutting themselves silk scarves from discarded American parachutes; the French student nurse going down to the beach to collect her forgotten swimsuit and discovering the beach full of British soldiers, among them her future husband.

What Beevor clearly realises, and what many of his competitors often forget, is that even the most savage campaign can soon become dull to read about. The trick, therefore, is to keep switching from the big picture to the tiny anecdote, from light to dark, and to keep the reader entertained with touches of character. Beevor needs only a few brush strokes to bring the key leaders and commanders alive, from Teddy Roosevelt Jr, with his walking stick, soft cap and disregard for danger, to the irrepressible George Patton, cheered by his troops as he promised to "cut the guts out of those Krauts" and personally shoot Hitler "just like I would a snake".

He is good on the Nazis, too: the elderly Field Marshal von Rundstedt, a Prussian aristocrat paralysed by lethargy and cynicism, or Hitler greeting the news of the invasion with glee, convinced that the Allies would be "smashed on the beaches". But in stark contrast to Hollywood war films, the Germans appear here as real people with virtues as well as vices. When a group of Birmingham lads was taken prisoner by some panzergrenadiers, they were astonished to be offered wine to drink, while their guards teased them about the likely failure of their landings and swapped photographs of their sweethearts.

What emerges above all from this thoroughly researched and gripping narrative, though, is the appalling human suffering of the struggle. Among the very first Allied troops in France, for example, were paratroopers dropped overnight, yet many were killed without firing a shot when they landed in flooded ditches and rivers. Many tank crewmen, too, died without reaching French soil when their tanks were launched too far from the beaches and sank like stones beneath the waves. On Omaha Beach, thousands of Americans were machine-gunned as they waded ashore, like ducks in a shooting gallery; later, as they inched their way south towards Paris, men had to use mess tins and spoons to scrape the charred remains of their comrades out of their tank shells. There was nothing glamorous about the battle for Normandy; most divisions lost more men every month than did the German and Soviet troops on the Eastern Front.

While Beevor's book on the Berlin campaign attracted criticism in Russia for its revelations about Red Army atrocities, it is from the US that he is likely to get flak this time. American GIs, as he shows, were no less courageous than their British and German counterparts, but the Americans were often poorly trained and liable to suffer shock as soon as they came under fire. Many were farm boys from the Midwest and almost comically anti-French; the general attitude was that you "couldn't trust them" and that all French women were sleeping with Germans. Beevor has a nice story about a French priest coming into his church and finding two soldiers from Alabama looting the poor box; they were, he suggests, just looking for souvenirs, although that was surely no consolation to the priest.

Despite all the patriotic American nonsense about the "greatest generation", Beevor shows that there were remarkably few heroes. There were rarely "more than a handful of men prepared to take risks and attack," he says; most men just wanted to get home in one piece and "somebody else to play the role of hero". Surveys showed that if a few broke ranks and fled, the rest would follow; in most engagements, as many as half never fired a shot. Even so, more than 200,000 Allied troops lost their lives in the battle for Normandy.

It was a turning point in the war and we are right to celebrate it. But the tragedy, as this splendid book makes clear, is that it came at such a cost.

• Dominic Sandbrook's most recent book is White Heat: A History of Britain in the Swinging Sixties (Abacus).